Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model

We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, ℝ)k WZNW model. In particular, the classical relations in SL(2, ℝ)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is ea...

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Autor principal: Bertoldi, G.
Otros Autores: Bolognesi, S., Giribet, G., Matone, M., Nakayama, Y.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2005
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030 |a NUPBB 
100 1 |a Bertoldi, G. 
245 1 0 |a Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model 
260 |c 2005 
270 1 0 |m Bertoldi, G.; Department of Physics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom 
506 |2 openaire  |e Política editorial 
504 |a Zamolodchikov, Al., Higher equations of motion in Liouville field theory hep-th/0312279; Bertoldi, G., Giribet, G., Zamolodchikov operator-valued relations for SL(2,ℝ)k WZNW model (2004) Nucl. Phys. B, 701, p. 481. , hep-th/0405094 
504 |a de Boer, J., Ooguri, H., Robins, H., Tannenhauser, J., String theory on AdS3 (1998) JHEP, 9812, p. 026. , hep-th/9812046 
504 |a Aharony, O., Gubser, S.S., Maldacena, J., Ooguri, H., Oz, Y., Large N field theories, string theory and gravity (2000) Phys. Rep., 323, pp. 183-386. , hep-th/9905111 
504 |a Maldacena, J., Ooguri, H., Strings in AdS3 and the SL(2,ℝ) WZW model. Part 1: The spectrum (2001) J. Math. Phys., 42, pp. 2929-2960. , hep-th/0001053 
504 |a Maldacena, J., Ooguri, H., Strings in AdS3 and the SL(2,ℝ) WZW model. Part 3: Correlation functions (2002) Phys. Rev. D, 65, p. 106006. , hep-th/0111180 
504 |a Matone, M., Uniformization theory and 2D gravity, 1: Liouville action and intersection numbers (1995) Int. J. Mod. Phys. A, 10, p. 289. , hep-th/9306150 
504 |a Bonora, L., Matone, M., KdV equation on Riemann surfaces (1989) Nucl. Phys. B, 327, p. 415 
504 |a Benoit, L., Saint-Aubin, Y., Degenerate conformal field theories and explicit expressions for some null vectors (1988) Phys. Lett. B, 215, p. 517 
504 |a Bauer, M., Di Francesco, P., Itzykson, C., Zuber, J.-B., Covariant differential equations and singular vectors in Virasoro representations (1991) Nucl. Phys. B, 362, p. 515 
504 |a Zograf, P., Takhtajan, L., On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces (1988) Math. USSR Sb., 60, pp. 297-313 
504 |a Takhtajan, L., Liouville theory: Quantum geometry of Riemann surfaces (1993) Mod. Phys. Lett. A, 8, p. 3529. , hep-th/9308125 
504 |a Matone, M., Quantum Riemann surfaces, 2D gravity and the geometrical origin of minimal models (1994) Mod. Phys. Lett. A, 9, p. 2871. , hep-th/9309096 
504 |a Matone, M., Nonperturbative model of Liouville gravity (1997) J. Geom. Phys., 21, p. 381. , hep-th/9402081 
504 |a Bonelli, G., Marchetti, P.A., Matone, M., Nonperturbative 2D gravity, punctured spheres and theta vacua in string theories (1994) Phys. Lett. B, 339, p. 49. , hep-th/9407091 
504 |a Bonelli, G., Marchetti, P.A., Matone, M., Algebraic-geometrical formulation of two-dimensional quantum gravity (1996) Lett. Math. Phys., 36, p. 189. , hep-th/9502089 
504 |a Takhtajan, L., Liouville theory: Ward identities for generating functional and modular geometry (1994) Mod. Phys. Lett. A, 9, p. 2293. , hep-th/9403013 
504 |a Takhtajan, L., Topics in quantum geometry of Riemann surfaces: Two-dimensional quantum gravity (1994) Como Quantum Groups, pp. 541-580. , hep-th/9409088 
504 |a Alvarez-Gaumé, L., Gómez, C., Topics in Liouville theory (1992) Proceedings of the 1991 Trieste Spring School on String Theory and Quantum Gravity, , J. Harvey (Eds.) World Scientific Singapore 
504 |a Ginsparg, P., Moore, G., Lectures on 2D Gravity and 2D String Theory, , hep-th/9304011 
504 |a Nakayama, Y., Liouville field theory: A decade after the revolution (2004) Int. J. Mod. Phys. A, 19, p. 2771. , hep-th/0402009 
504 |a Aganagic, M., Klemm, A., Marino, M., Vafa, C., The topological vertex hep-th/0305132; Aganagic, M., Dijkgraaf, R., Klemm, A., Marino, M., Vafa, C., Topological strings and integrable hierarchies hep-th/0312085; Bonora, L., Lugo, A., Matone, M., Russo, J., A global operator formalism on higher genus Riemann surfaces: B-C systems (1989) Commun. Math. Phys., 123, p. 329 
504 |a Gervais, J.-L., Neveu, A., The dual string spectrum in Polyakov's quantization, 1 (1982) Nucl. Phys. B, 199, p. 59 
504 |a Gervais, J.-L., Neveu, A., Dual string spectrum in Polyakov's quantization, 2: Mode separation (1982) Nucl. Phys. B, 209, p. 125 
504 |a Gervais, J.-L., Neveu, A., New quantum treatment of Liouville field theory (1983) Nucl. Phys. B, 224, p. 329 
504 |a Gervais, J.-L., Neveu, A., Novel triangle relation and absence of tachyons in Liouville string field theory (1984) Nucl. Phys. B, 238, p. 125 
504 |a Gervais, J.-L., Neveu, A., Green functions and scattering amplitudes in Liouville string field theory, 1 (1984) Nucl. Phys. B, 238, p. 396 
504 |a Gervais, J.-L., Neveu, A., Locality in strong coupling Liouville field theory and string models for seven-dimensions, thirteen-dimensions and nineteen-dimensions (1985) Phys. Lett. B, 151, p. 271 
504 |a Gervais, J.-L., The quantum group structure of quantum gravity in two-dimensions (1990) Proceedings, Random Surfaces and Quantum Gravity Cargese, pp. 347-361. , see High Energy Physics Index 30 1992 No. 17911 
504 |a Teschner, J., Liouville theory revisited (2001) Class. Quantum Grav., 18, pp. R153-R222. , hep-th/0104158 
504 |a Teschner, J., Quantum Liouville theory versus quantized Teichmüller spaces (2003) Fortschr. Phys., 51, p. 865. , hep-th/0212243 
504 |a Teschner, J., On the relation between quantum Liouville theory and the quantized Teichmüller spaces hep-th/0303149; Teschner, J., A Lecture on the Liouville Vertex Operators, , hep-th/0303150 
504 |a Teschner, J., From Liouville theory to the quantum geometry of Riemann surfaces hep-th/0308031; Maldacena, J.M., The large N limit of superconformal field theories and supergravity (1998) Adv. Theor. Math. Phys., 2, pp. 231-252 
504 |a Maldacena, J.M., (1999) Int. J. Theor. Phys., 38, pp. 1113-1133. , hep-th/9711200 
504 |a Maldacena, J.M., Strominger, A., AdS3 black holes and a stringy exclusion principle (1998) JHEP, 9812, p. 005. , hep-th/9804085 
504 |a Giveon, A., Kutasov, D., Seiberg, N., Comments on string theory on AdS3 (1998) Adv. Theor. Math. Phys., 2, p. 733. , hep-th/9806194 
504 |a Kutasov, D., Seiberg, N., More comments on string theory on AdS3 (1999) JHEP, 9904, p. 008. , hep-th/9903219 
504 |a Ponsot, B., Teschner, J., Liouville bootstrap via harmonic analysis on a non-compact quantum group hep-th/9911110; Ponsot, B., Teschner, J., Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of Uq(sl(2,ℝ)) (2001) Commun. Math. Phys., 224, pp. 613-655. , math.QA/0007097 
504 |a Awata, H., Yamada, Y., Fusion rules for the fractional level sl(2) algebra (1992) Mod. Phys. Lett. A, 7, p. 1185 
504 |a Di Francesco, P., Itzykson, C., Zuber, J.-B., Classical W-algebras (1991) Commun. Math. Phys., 140, p. 543 
520 3 |a We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, ℝ)k WZNW model. In particular, the classical relations in SL(2, ℝ)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS3/ CFT2 correspondence. Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so-called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2, ℝ)k. The solutions of the jth classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2, ℝ). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2, ℝ), which is interpreted as the isometry group of the hyperbolic upper half-plane. © 2005 Elsevier B.V. All rights reserved.  |l eng 
536 |a Detalles de la financiación: Fundación Antorchas 
536 |a Detalles de la financiación: Universidad de Buenos Aires, HPRN-CT-2000-00131 
536 |a Detalles de la financiación: Ministry of Education, Culture, Sports, Science and Technology 
536 |a Detalles de la financiación: We would like to thank Giulio Bonelli, Juan Maldacena and Luca Mazzucato for discussions. G. Bertoldi is supported by the Foundation BLANCEFLOR Boncompagni-Ludovisi, née Bildt. G. Giribet is supported by the Institute for Advanced Study and Fundación Antorchas (on leave from Universidad de Buenos Aires). M. Matone is partially supported by the European Community's Human Potential Programme under contract HPRN-CT-2000-00131 Quantum Spacetime. Y. Nakayama is supported in part by a Grant for 21st Century COE Program “QUESTS” from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Appendix A 
593 |a Department of Physics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom 
593 |a Scuola Normale Superiore, Piazza Dei Cavalieri 7, 56126 Pisa, Italy 
593 |a INFN, Sezione di Pisa, Pisa, Italy 
593 |a Universidad de Buenos Aires, Ciudad Universitaria 1428, Pabellon I, Buenos Aires, Argentina 
593 |a Dipartimento di Fisica G. Galilei, Università di Padova, Via Marzolo 8, 35131 Padova, Italy 
593 |a INFN, Sezione di Padova, Padova, Italy 
593 |a Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan 
700 1 |a Bolognesi, S. 
700 1 |a Giribet, G. 
700 1 |a Matone, M. 
700 1 |a Nakayama, Y. 
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